Do all those fine folks on Twitter represent a good cross-section of the general public?

Overall, the reaction to political events on Twitter reflects a combination of the unique profile of active Twitter users and the extent to which events engage different communities and draw the comments of active users. While this provides an interesting look into how communities of interest respond to different circumstances, it does not reliably correlate with the overall reaction of adults nationwide.

tl;dr: Not so much:

At times the Twitter conversation is more liberal than survey responses, while at other times it is more conservative. Often it is the overall negativity that stands out. Much of the difference may have to do with both the narrow sliver of the public represented on Twitter as well as who among that slice chose to take part in any one conversation.

The Pew Research Centre report on Twitter reaction to events makes for fascinating reading.